Nonnormal distribution of Benford errors for integer sequences a^n

Let $a\geq 2$ be an integer that is not a power of $10$, let $d\in\{1,2,\dots,9\}$, and let $E_d(N,\{a^n\})$ denote the Benford error. Nonnormal distribution conjecture for Benford errors. The sequence of errors does not satisfy a central limit theorem in the sense that there do not exist sequences $\{A_N\}$ and $\{B_N\}$ for which the normalized empirical distribution converges to the standard normal distribution. The conjecture is motivated by the fact that the continued-fraction Lindeberg condition is known to fail for almost every real number, but the source gives no resolution for $\log_{10}a$ when $a$ is an integer not a power of $10$.